Three adults and three children are to be seated at a circular table. In how many different ways can they be seated if each child must be next to two adults? (Two seatings are considered the same if one can be rotated to form the other.)

xxyoohoo Oct 5, 2023

#1**0 **

To seat three children at a circular table such that each child must be next to two adults, we can create a sequence of three adults and three children in which each child is in between two adults. There are 6! ways to arrange the adults and children in a sequence. However, we have overcounted the number of arrangements by a factor of 3, since we have counted each arrangement as if the children were distinguishable.

Therefore, the total number of ways to seat the three adults and three children at a circular table such that each child must be next to two adults is:

6!/3 = \boxed{240}.

bingboy Oct 6, 2023